3 L water is taken out from vessel full of water and substituted by pure milk. This process is repeated two more times. Finally, the ratio of milk and water in the solution becomes 1728 : 27. Find the volume of the original solution.

We use formula for it where
n = number of time process of out going repeated.
y = Out going milk in process.
x = Volume of original solution.
F = Final milk left in mixture.
$$F = x{\left( {1 - \frac{y}{x}} \right)^n}$$
Final quantity of water,
$$F = x{\left( {1 - \frac{3}{x}} \right)^3}$$
$$\frac{F}{x} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{{27}}{{1728}} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$${\left( {\frac{3}{{12}}} \right)^3} = {\left( {\frac{{x - 3}}{x}} \right)^3}$$
$$\frac{3}{{12}} = \frac{{x - 3}}{x}$$
$$x = 4 \,\text{L}$$